Let x be given.

Assume Hx.

Apply xm (0 ≤ x) to the current goal.

Assume H1.

rewrite the current goal using nonneg_abs_SNo x H1 (from left to right).

An exact proof term for the current goal is Hx.

Assume H1.

rewrite the current goal using not_nonneg_abs_SNo x H1 (from left to right).

Apply SNo_minus_SNo to the current goal.

An exact proof term for the current goal is Hx.

∎